Suppose that the random variables X1, , Xk are independent and that Xi has the negative binomial distribution with parameters ri and p (i 1 k) Prove that the sum X1 Xk has the negative binomial distribution with parameters r r1 rk and p ...

By Eq 556 the mgf of X i is Therefore the mgf ...

Suppose that the random variables X1, . . . , Xk are independent and that Xi has

Question:

Suppose that the random variables X1, . . . , Xk are independent and that Xi has the negative binomial with parameters ri and p (i = 1 . . . k). Prove that the sum X1 + . . . + Xk has the negative binomial with parameters r = r1 + . . . + rk and p.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...